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\(\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times...\times\dfrac{x-1}{x}=\dfrac{1010}{1011}\)
\(\dfrac{3\times4\times5\times...\times\left(x-1\right)}{4\times5\times6\times...\times x}=\dfrac{1010}{1011}\)
\(\dfrac{3}{x}=\dfrac{1010}{1011}\)
\(x=\dfrac{3\times1011}{1010}=3\)
Dãy số 1; 6; 11; ...; 96 có: ( 96 -1 ) : 5 + 1 = 20 số
(x + 1 ) + (x + 6 ) +(x + 11) +...+ ( x +96) =1010
(x + x + x +...+ x ) + ( 1 + 6 + 11+...+ 96 ) = 1010
\(20\times x+\left(96+1\right).20:2=1010\)
\(20\times x+970=1010\)
\(20\times x=1010-970\)
\(20\times x=40\)
\(x=2\)
Ta có : (x+1)+(x+6)+(x+11)+...+(x+96) =1010
=>x+1+x+6+x+11+...+x+96=1010
=>(x+x+x+...+x)+(1+6+11+...+96)=1010
=>20×x+(1+96)×20÷5=1010
=>20×x+388=1010
=>20×x=622
=>x=622÷20
=>x=31,1
1+2+3+4+5+6+7+8+9+...........+99=X+1+2+3+4+5+6+7+8+9+.................+99
4950=4950+X
X=4950-4950
X=0
ta có M = 6/2*3 + 6/3*4 + ... +6/99*100
= 6* (1/2*3 + 1/3*4 + ... +1/99*100)
= 6* ( 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/99 - 1/100)
= 6* ( 1/2 - 1/100 )
= 6* 49/100 = 147/50
vậy M= 147/50
Do M = 6:2x3 + 6: 3x4 +......+6:99x100
=> M =\(\frac{6}{2.3}+\frac{6}{3.4}+........+\frac{6}{99.100}\)
M = \(6.\left(\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\right)\)
M =\(6.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{99}-\frac{1}{100}\right)\)
M = \(6.\left(\frac{1}{2}-\frac{1}{100}\right)\)
M = \(6.\frac{49}{50}\)
M = \(\frac{147}{25}\)
(1-2+3-4+.....-98+99)x(2013x6-2013-2013x5)
=(1-2+3-4+....-98+99)x[ 2013x(6-1-5)]
= (1-2+3-4+....-98+99)x(2013x0)
= (1-2+3-4+....-98+99)x0 = 0
\(x.\left[\left(6+6+6\right):3\right]+99=100\)
\(x.\left(18:3\right)+99=100\)
\(6x+99=100\)
\(6x=1\)
\(x=\frac{1}{6}\)
Vậy \(x=\frac{1}{6}\)
\(x\times\left(18:3\right)+99=1010\)
\(x\times6=1010-99=911\)
x=911:6
\(x=\frac{911}{6}\)